A novel multi-distribution multi-state flow network and its reliability optimization problem

• Published in: Reliability engineering & system safety Vol. 176; pp. 209 - 217
• Main Authors: Yeh, Wei-Chang, Chu, Ta-Chung
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01.08.2018; Elsevier BV
• Subjects: Algorithms; Allocations; Budget allocation; Budgeting; Distribution engineering; Multi-distribution; Multi-state flow network (MFN); Network flow problem; Network reliability; Optimization; Reliability engineering; State distribution; Systems analysis; Multi-state flow network (MFN); Multi-distribution; Budget allocation; State distribution
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2018.04.006

•A novel budget-allocation multi-distribution MFN reliability problem is defined.•A new algorithm is proposed for such problems using 3 novel concepts listed below.•The novel critical budget allocated vector and its algorithm (DFS-BB) are proposed.•The novel maximal d-MP set (i.e., Pmax) is proposed.•A new and fast d-MP algorithm is proposed to find all d-MPs based on Pmax. The traditional multi-state flow network (MFN) reliability problem is a well-known NP-hard problem, and has been an active area of research for the past four decades. In the MFN reliability problem, the state distribution, i.e. the states and the occurrence probabilities of each arc, is known and fixed. However, the notations used in the MFN problems never considered the state distribution. In addition, each arc has only one state distribution, and this limits the application of the MFN. Thus, the notations relating to the state distribution are added or redefined in this study, and a novel budget-allocation multi-distribution MFN reliability problem is defined and proposed by considering networks with more than one state distribution under different budget allocations. Furthermore, a new algorithm is proposed to solve the proposed novel NP-Hard problem. The correctness and time complexity of the proposed algorithm are analyzed, and one benchmark example is given to demonstrate how to optimize the budget-allocation multi-distribution MFN reliability under different budget constraints.